Question

# MCQ
DESCRIPTION
Consider three friends Jake, Hitchcock and Scully who work at
different speeds
. When the fastest two persons among them pair
up they take x days to finisha task. When the slowest troof them
pair-up they take ydays to finish a task. If one of them workedal
by himself
, he would take thrice the time as it would take when all
0
the three friends worked together. How much time would take
02
all three friends worked together.
REPORTANZARE
01​

Answer 1

Answer:

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Answer 2

Answer:

$\frac{4mn} {3(m+n)}$would take all three friends worked together

Step-by-step explanation:

Let Jake<Hitchcock<scully in terms of efficiency

Hitchcock and scully together take n days

Jake and Hitchcock together take m days

one of them if he worked alone would take thrice as much time as it would take when all three work together

This is crucial statement. Now if there are three people who are all equally efficient for each of them it would take thrice as much time as for all three together

Now , this tell us that the person who takes thrice as much times cannot be the quickest  one. If the quickest one is only one-third as efficient as the entire team, the other two cannot add up to two-thirds. By similar  logic, the slowest one cannot be the person who is one-third as efficient.

In other words the person one third as efficient =B

Let Jake, Hitchcock, scully together take x days. Hitchcock alone would take 3x days.

Hitchcock, scully together take n days. Or Hitchcock+ scully in 1 day do

1/n of the task-----Equation 1

Jake, Hitchcock together take m days. or Jake+ Hitchcock in 1 day do

1/m of the task ---------equation 2

Hitchcock takes 3x days to do the task or Hitchcock in one day does 1/3x of the task --------Equation 3

Now if we do 1+2-3

Jake + Hitchcock + scully do

$\frac{1}{n}+\frac{1}{m}-\frac{1}{3x}$ in a day. This should be equal to 1/x as all three of them complete the task in x days

$\frac{1}{n}+\frac{1}{m}-\frac{1}{3x}=\frac{1}{x}$

$\frac{1}{n}+\frac{1}{m}=\frac{4}{3x}$

$\frac{m+n}{mn} =\frac{4}{3x}$

$\frac{4mn} {3(m+n)}$